Skip American judge we must think not quite appropriate (4,4)

I believe the answer is:

jump rope

I'm a little stuck... Click here to teach me more about this clue!

'skip american judge we' is the definition.
I can't tell whether this defines the answer.

'must think not quite appropriate' is the wordplay.
'must think' becomes 'jum' (I can't explain this - if you can you should give a lot more credence to this answer).
'not quite' means to remove the last letter (most but not all of the word).
'appropriate' becomes 'proper' (similar in meaning).
'proper' with its final letter taken away is 'prope'.
'jum'+'prope'='JUMP ROPE'

Can you help me to learn more?

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.